Answer:
[tex]2\sqrt{65}[/tex] cm, decimal form is about 16.1 cm
Step-by-step explanation:
Use the pythagorean theorem:
A^2 + B^2 = C^2
A and B are legs, c is hypotenuse
First leg is 16, second leg is 2
Plug it in:
16^2 + 2^2 = hypotenuse^2
256 + 4 = hypotenuse ^2
260 = h^2
[tex]\sqrt[2]{260}[/tex] = h
To simplify the square root of 260, we can factor 260 into its prime factors:
260 = 2 x 2 x 5 x 13
Then, we can take out the pairs of identical factors from under the square root symbol:
sqrt(260) = sqrt(2 x 2 x 5 x 13)
= sqrt(2 x 2) x sqrt(5) x sqrt(13)
= 2sqrt(65)
[tex]2\sqrt{65}[/tex]
Answer:
16.2 or 16.00
Step-by-step explanation:
Leg #1 --->16
Leg #2 --->2
C ---> hypotenuse
16.12452---->16.12
16.12 rounded to the nearest tenth is 16.00
If a square has an area of 94 square units. How big is its side length?
The requried side length of the square is approximately 9.695 units.
To find the side length of a square with an area of 94 square units, we need to take the square root of the area.
a² = 94
a = √94
a ≈ 9.695
Therefore, the side length of the square is approximately 9.695 units.
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10PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED
the scatter graph shows the maximum temperature and the number of hours of sunshine in 13
The coordinates of the point which is an outlier would be ( 14, 13).
The correlation between the 13 British towns is Linear.
The number of hours of sunshine for the British town with the maximum of 17.4 degrees Celsius is 13 hours of sunshine.
How to find the hours of sunshine ?The coordinates of the outlier would be ( 14, 13). This is because, that point on the graph is far from the other points and does not follow their correlation.
The rest of the towns seem to be increasing in the same direction so they are linear.
The number of hours of sunshine in the British town with the maximum temperature of 17.4 degrees Celsius, based on the line of best fit drawn, would be 13 hours of sunshine.
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Full question is:
The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.
A line of best fit has also been drawn.
One of the points in an outliner.
a) Write down the coordinates of this point. (1)
b) For all the other points write down the type of correlation in just one word. (1)
On the same day, in another British town, the maximum temperature was 17.4C.
c) Estimate the number of hours of sunshine in this town on this day. (2)
Change the function f(x)=2x^2+4x+3 into vertex form.
Answer:
f(x) = 2(x + 1)² + 1
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms
= 2(x² + 2x) + 3
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 2x
f(x) = 2(x² + 2(1)x + 1 - 1) + 3
= 2(x + 1)² - 2(1) + 3
= 2(x + 1)² - 2 + 3
= 2(x + 1)² + 1 ← in vertex form
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
The graph that correctly displays the data is this: C. bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.
How to obtain the correct graphA graph plots values to show the relationship between two variables often depicted by the x and y axes. The correct graph to display this data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students."
The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.
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(-4,-6) and (8,9). Slope
slope= y2 - y1/ x2 - x1 ( take (-4, -6) as 1 and (8,9) as 2 where 9 and -6 are y2 and y1 respectively and 8 and -4 as x2 and x1 respectively)
- slope = 9 - (-6) / 8 - (-4)= 9 + 6/ 8 + 4
- slope = 15 / 12 (simplify)
- slope = 5/ 4
a company decides to keep a huge shipment of light bulbs if p<5% are defective otherwise they return the shipment. after running a test the company decides to keep the shipment and after all the bulbs where used it was found that less than 5% of the bulbs were defective. what type of error could have occurred?
The type of error that could have occurred in this scenario is a Type II error. A Type II error occurs when the null hypothesis is not rejected, even though it is false.
In this case, the null hypothesis is that the proportion of defective bulbs in the shipment is greater than or equal to 5%. By not rejecting this null hypothesis, the company is accepting the possibility that the shipment has a high proportion of defective bulbs, when in reality it does not. This can lead to significant costs for the company, such as the cost of returning the shipment or the cost of replacing defective bulbs in the future.
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assume the triangle has the given measurements. Solve for the remaining sides and angles.
The missing angles are sides are;
a = 9.8 B = 60 degreesC = 90 degreesHow do you solve a triangle?We can see that we would have to first apply the cosine rule here;
[tex]a^2 = b^2 + c^2 - 2abCos A\\a^2 = (17)^2 + (19.6)^2 - 2(17 * 19.6)Cos 30\\a^2 = 673.16 - 666.4Cos 30[/tex]
a = 9.8
We can now apply the sine rule to obtain the angle B
[tex]a/Sin A = b/Sin B\\SinB = bSin A/a\\B = Sin-1 ( bSin A/a)\\B = Sin-1(17 * Sin 30/9.8)[/tex]
B = 60
Then;
C = 180 - (30 + 60)
C = 90 degrees
Thus the triangle in the problem have been solved.
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Find the value of x
33 degrees and 108 degrees
Answer:
141 degrees
Step-by-step explanation:
First find the value of the other interior angle that is not shown. To find it u add 108 n 33 which gives you 141
Then subtract 141 from 180 which gives u 39 degrees
After subtract 39 from 180 which gives you 141 degrees
in the newspaper article referred to in exercise 9.57, 32% of the 1600 adults polled said the u.s. space program should emphasize scientific exploration. how large a sample of adults is needed for the poll if one wishes to be 95% confident that the estimated per- centage will be within 2% of the true percentage?
What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 less than or equal to x less than or equal to 3
The correct list of functions ordered from 0 ≤ x ≤ 3 is:
h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x
Line connecting the interval's endpoints in order to compute the average rate of change for each function over range 0 x 3.
For f(x) = x^2, the slope between x = 0 and x = 3 is:
[tex](f(3) - f(0)) / (3 - 0) = (9 - 0) / 3 = 3[/tex]
For g(x) = 2x + 1:
[tex](g(3) - g(0)) / (3 - 0) = (7 - 1) / 3 = 2[/tex]
For h(x) = sin(x):
[tex](h(3) - h(0)) / (3 - 0) = (sin(3) - sin(0)) / 3[/tex] ≈ 0.279
For k(x) = e^x, the slope between x = 0 and x = 3 is:
[tex](k(3) - k(0)) / (3 - 0) = (e^3 - 1) / 3[/tex] ≈ 6.076
Therefore, correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3 is:
[tex]h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x[/tex]
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--The complete Question is, Consider the following four functions:
f(x) = x^2
g(x) = 2x + 1
h(x) = sin(x)
k(x) = e^x
What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3? --
3. A function can have zero to many parameters, and it can return this many values.a. zero to manyb. noc. only oned. a maximum of tene. None of these
A function can have zero to many parameters, and it can return only one (option c).
In mathematics, a function is a rule that maps each element from one set, called the domain, to a unique element in another set, called the range.
The number of parameters a function can take determines the number of arguments required to call the function.
For instance, a function f(x) takes one parameter, and it requires one argument to be called.
On the other hand, a function g(x,y,z) takes three parameters, and it requires three arguments to be called. However, a function h() takes no parameters and does not require any argument to be called.
Hence the correct option is (c).
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below you are given a partial excel output based on a sample of 16 observations. anova df ss ms f regression 4,853 2,426.5 residual 485.3 coefficients standard error intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 the t value obtained from the table that is used to test an individual parameter at the 1% level is . a. 2.921 b. 2.977 c. 2.65 d. 3.012
To discover the t-value for testing a person parameter at the 1% level, we ought to isolate the coefficient appraise by its standard deviation and compare it to the t-distribution with suitable degrees of flexibility.
For case, to test the parameter gauge for x1, we would calculate the t-value as: t = (-3.682) / 2.630 ≈ -1.4
At that point compare this t-value to the t-distribution with 485 degrees of flexibility (which compares to the leftover degrees of opportunity), and decide on the off chance that it surpasses the basic esteem at the 1% level (which is around 2.977).
In any case, the given yield does not demonstrate which parameter appraise is being tried, so we cannot decide the comparing t-value. Hence, none of the reply choices are rectified.
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Find the vectors that join the center of a clock to the hours 1:00, 2:00, and 3:00. Assume the clock is circular with a radius of 1 unit.
at
1:00
2:00
3:00
The vectors that join the center of a clock to the hours :
At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)
At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)
At 3:00: (cos(π/2), sin(π/2)) = (0, 1)
What is Vector?
A vector is a object that has both magnitude (size) and direction. In other words, a vector is a quantity that can be represented by an arrow or line segment, where the length of the arrow corresponds to the magnitude of the vector.
To find the vectors that join the center of a clock with radius 1 unit to the hours 1:00, 2:00, and 3:00, we can use basic trigonometry.
First, we can find the angle (in radians) between the 12:00 position and each of the desired hour positions. Since there are 12 hours on a clock and the circle has a circumference of 2πr = 2π(1) = 2π, the angle between each hour mark is:
2π/12 = π/6 radians
Therefore, the angles between the center of the clock and the hour marks are:
At 1:00, the angle is π/6 radians clockwise from the 12:00 position.
At 2:00, the angle is 2π/6 = π/3 radians clockwise from the 12:00 position.
At 3:00, the angle is 3π/6 = π/2 radians clockwise from the 12:00 position.
Next, we can use the cosine and sine functions to find the x and y components of each vector. The x-component of each vector is given by the radius times the cosine of the angle, and the y-component is given by the radius times the sine of the angle.
Therefore, the vectors that join the center of the clock to the hours 1:00, 2:00, and 3:00 are:
At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)
At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)
At 3:00: (cos(π/2), sin(π/2)) = (0, 1)
Note that these vectors are unit vectors, meaning that they have a length of 1 unit.
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Austin collected 30 9/10 kg of glass for music going exactly 2/3 of the glass he collected was blue glass. What was the total amount in kilograms of blue class Austin collected
Answer:
20 3/5
Step-by-step explanation:
this is the correct result when 30 9/10 is multipled by 2/3
Write the transformation matrix and the resultant matrix that will translate the triangle, (-2, 4), given the triangles vertices are at A(-1, 3), B(0, -4) and C(3, 3).
The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
Define translationIn mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.
To translate the triangle by a vector (x, y), we use the following transformation matrix:
|1 0 x|
|0 1 y|
|0 0 1|
For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:
|1 0 -2|
|0 1 4 |
|0 0 1 |
To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:
| -1 | | 1 0 -2 | | -3 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
| 0 | | 1 0 -2 | | -2 |
| -4 | -> | 0 1 4 | = | 0 |
| 1 | | 0 0 1 | | 1 |
| 3 | | 1 0 -2 | | 1 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
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Explain how you would find the highest point the rider achieved on this jump.
A. What would be the two quantities you would measure for x and y?
B. What would your equation possibly look like? Put the picture on a grid and show some possible points
C. What points could you use to find the maximum height? How would you use those points? Be specific
Answer:
Step-by-step explanation:
36
1870003# gave an answer about Sean and his aquarium in ratios. He had 7 guppies to 12 cichlids which came out to be 7:12 and 4 tetras to 11 catfishes in ratios it is 4:11 and lastly he had a ratio of corydoras catfishes 9 to the total number of fishes is how many ratio to the total number of fish? I had 11:34 is that right?
The simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.
How to find the the ratioTo find the ratio of corydoras catfishes to the total number of fish, we need to add up the number of corydoras catfishes to the total number of fish, and express the ratio as a simplified fraction.
The total number of fish is 7 + 12 + 4 + 11 = 34.
The ratio of corydoras catfishes to the total number of fish is 9:34.
To simplify this ratio, we can divide both sides by the greatest common factor, which is 1 in this case.
So the simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.
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A circle has a center of (1, -1). The circumference passes through (1, 2). Find the length of the circumference of the circle. Use 3.14 for pi. Then, Find the area of the circle.
Answer:
The radius of the circle is 3, so
Circumference = 2(3)π = 6π = 18.84
Area = π(3^2) = 9π = 28.26
Find the area of the figure. Round to the nearest tenth, if necessary.
From the given dimensions, area of the figure is approximately equal to 75.8 cm².
What is a regular polygon?A regular polygon is a closed shape with straight sides and equal-length edges, as well as equal angles between those sides. Examples of regular polygons include equilateral triangles, squares, and hexagons. The number of sides a regular polygon has is referred to as its order, while the measure of each interior angle of a regular polygon can be calculated using the formula (n-2) x 180/n, where n represents the number of sides.
From the image we can see that, ABHI is a square with sides 6 cm, BCDGH is a regular pentagon with sides 6 cm (BH = AI = 6 cm) and DEFG is a rectangle with length 11 cm and breadth 6 cm ( DG = AI = 6 cm).
To find the area of the figure we have to find the area of each shape and add it together.
Area of square = side × side = 6 × 6 = 36 cm²
Area of regular pentagon = [tex]\frac{1}{4} \sqrt{5(5+25)a^{2} }[/tex]
= [tex]\frac{1}{4} \sqrt{5(5+25)6^{2} }[/tex]
= [tex]\frac{1}{4} \sqrt{25 + 10*1.41*36}[/tex]
= [tex]\frac{1}{4} \sqrt{532.6 }[/tex]
≈ 5.77 cm²
Area of rectangle = 2(l + b) = 2(11 + 6) = 34 cm²
Therefore area of the figure = 36 cm² + 5.77 cm² + 34 cm² ≈ 75.8 cm².
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help me asap
pls i need to find z this R.4 ixl for special right triangles
Answer:
3 cm
Step-by-step explanation:
because the correct answer is 3cm
a study on children diagnosed with deliops disease examined whether taking garlic pills would prolong the life of the children. the 50 children who did not take garlic lived an average of 4 years. the 40 children who took the garlic pills lived an average of 21 years. the confidence interval for the difference in average for the non-garlic pills verses garlic pills was (-43, 9) years. what would you conclude about the effectiveness of garlic pills?
The confidence interval for the difference in average lifespan between the two groups of children (-43, 9) years includes 0, which means that we cannot conclude with confidence that there is a significant difference between the two groups.
Since the confidence interval includes negative values, we cannot even conclude that the garlic pills were beneficial in prolonging the life of the children. It is possible that the garlic pills had no effect or even a harmful effect on the lifespan of the children.
Therefore, based on this information, we cannot conclude that garlic pills are effective in prolonging the life of children with deliops disease. Further research would be needed to determine whether garlic pills have any beneficial effects on the lifespan of these children.
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a rancher has 10,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures, with an internal fence parallel to one of the rectangular sides. what is the maximum area of each pasture? round to the nearest square foot.
For a 10,000 linear feet of fencing and wants to enclose a rectangular field, the maximum area of each pasture is equals to the 2,083,333.33 square feet .
A rancher wants to enclose about 10,000 linear feet of fencing in a rectangular field. There are two equal pastures. Let, W the Width and L the Length with 3 pieces. The total length will be equal to 2W + 3L. As we know, the Area of rectangle, A = L×W ---(1)
Perimeter of rectangle = 10,000 feet, so sum of all sides of rectangle, 2W + 3L = 10000
Solve for determining value of L, 3L
= 10000 - 2W
[tex]L = \frac{ 10000 - 2W }{3}[/tex]
Substitutes for L into the first equation, A = L×W
[tex]A = W(\frac{ 10000 - 2W }{3})[/tex]
For maximum area, set the 1st derivative = 0.
differentiating above Area equation w.r.t W,[tex] A = \frac{(10000 \: W - 2W^2)}{3}[/tex]
[tex] \frac{dA}{dW} = \frac{d(\frac{10000 \: W - 2W^2}{3})}{dW}[/tex]
=> [tex]\frac { 1}{3}(10000 - 4W) = 0 [/tex]
=> W = 2500 meters
Now, using above relation, 2W + 3L= 10000
=> 5000 + 3L = 10000
=> 3L = 5000
=> L = 1667 meters
Area = 2500× 5000/3 = 4,166,666.67 sq feet. Now, maximum area of each pasture
= 4,166,666.67/2 = 2,083,333.33333 sq. feet. Hence, required value is 2,083,333.33 sq. feet.
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Bret bought his family lunch. Before tax, the bill came to $42. The sales tax was 6% and Bret tipped the waitress 20% before tax was added. How much money did Bret spend?
Answer: Bret spent $52.92 on the lunch, including tax and tip.
Step-by-step explanation:
Given:
The bill before tax = $42
Sales tax = 6%
Tip = 20% before tax
To find:The total amount of money Bret spent
Solution: Calculate the sales tax:
Sales tax = 0.06 * $42 = $2.52
Calculate the total bill, including tax:
Total bill = $42 + $2.52 = $44.52
Calculate the bill before tax, based on which the tip is calculated:
Bill before tax = $44.52 - $2.52 = $42
Calculate the tip amount:
Tip = 0.2 * $42 = $8.40
Calculate the total amount spent by Bret:
Total spent = $44.52 + $8.40 = $52.92
Therefore, Bret spent $52.92 on the lunch, including tax and tip.
I just need an answer to this. I’ve tried everything I’ve erased so much, my paper is starting to wear out.
Answer:
2x²- 10x + 8
3x² - x - 4
Step-by-step explanation:
Answer:
hope this helps..........
what is 55/63 in simplest form
55/63 is already in its simplified form.
To simplify 55/63, we can divide both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 55 and 63, we can use prime factorization:
55 = 5 × 11
63 = 3 × 3 × 7
The common factors of 55 and 63 are 1, so the GCF is 1. We can divide both the numerator and denominator by 1:
55/1/63/1
Therefore, 55/63 in simplest form is 55/63.
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How did knowing what addition and subtraction mean help you figure out how the value of an expression can decrease even if the value of a variable increases?
Understanding the meaning of addition and subtraction will allows us to make predictions about how changing the value of a variable will affect the value of an expression.
What are integers?In mathematics, integers are a set of whole numbers that include both positive and negative numbers, as well as zero. The set of integers is denoted by the symbol Z, and it includes all the natural numbers (1, 2, 3,...), their negatives (-1, -2, -3,...), and zero (0). Integers are used in a variety of mathematical contexts, including algebra, number theory, and geometry. Integers can be used to represent many real-world situations, such as temperatures above or below zero, changes in altitude, gains or losses in money, and more. They are also used extensively in computer programming and other fields that rely heavily on mathematics.
Knowing what addition and subtraction mean allows you to understand how changing the value of a variable can affect the value of an expression.
For example, consider the expression x + 2. If x has a value of 3, then the value of the expression is 5. However, if x increases to 4, then the value of the expression increases to 6. This is because we are adding 2 to the value of x.
On the other hand, if we have the expression x - 2 and x has a value of 3, then the value of the expression is 1. If x increases to 4, then the value of the expression decreases to 2. This is because we are subtracting 2 from the value of x, so as x increases, the value of the expression decreases.
Understanding the meaning of addition and subtraction is essential to be able to manipulate expressions and variables, and it allows us to make predictions about how changing the value of a variable will affect the value of an expression.
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Can you pls help? This is geometry
The equation of the circle is (x - 2)²+ (y - 3)² = 169
Define circleA circle is a two-dimensional form that may be described as a collection of points that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.
The following is the equation for a circle with centres (a, b) and radius r:
(x - a)² + (y - b)² = r²
In this case, the center of the circle is A(2,3), and a point on the circle is B(7,15). The radius of the circle may be calculated using the distance formula:
r = √((7 - 2)² + (15 - 3)²) = √(5² + 12²) = 13
So the equation of the circle is:
(x - 2)² + (y - 3)² = 13²
(x - 2)²+ (y - 3)² = 169
Therefore, the equation of the circle is (x - 2)²+ (y - 3)² = 169
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suppose that ann selects a ball by first picking one of two boxes at random and then selecting a ball from this box. the first box contains three orange balls and four black balls, and the second box contains seven orange balls and four black balls. what is the probability that ann picked a ball from the second box if she has selected an orange ball? (enter the value of the probability in decimal format and round the final answer to two decimal places.)
The probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).
We can use Bayes' theorem to calculate the probability that Ann picked a ball from the second box given that she selected an orange ball.
Let A be the event that Ann selected an orange ball, and B be the event that Ann picked a ball from the second box. We want to find P(B|A), the probability that Ann picked a ball from the second box given that she selected an orange ball.
We know that there are two boxes, each with a probability of 1/2 of being selected. The probability of selecting an orange ball from the first box is 3/7, and the probability of selecting an orange ball from the second box is 7/11. Therefore, the probability of selecting an orange ball overall is:
P(A) = P(A|B)P(B) + P(A|B')P(B')
= (7/11)(1/2) + (3/7)(1/2)
= 25/42
Now we can use Bayes' theorem:
P(B|A) = P(A|B)P(B)/P(A)
= (7/11)(1/2)/(25/42)
= 14/25
Therefore, the probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).
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The number of outcomes that are in the sample space = 20
The number of outcomes that are in the event = 5
How to calculate the probability of the selected events?To calculate the probability of an event, the formula that should be used is given as follows;
Probability = possible event/sample space.
possible outcome = 5
sample space = 20
Probability = 5/20 = 1/4
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